Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.3 Complex Numbers - 1.3 Exercises - Page 112: 74



Work Step by Step

$\dfrac{14+5i}{3+2i}$ Begin the evaluation of the quotient by multiplying the numerator and the denominator by the complex conjugate of the denominator: $\dfrac{14+5i}{3+2i}\cdot\dfrac{3-2i}{3-2i}=\dfrac{(14+5i)(3-2i)}{3^{2}-(2i)^{2}}=...$ Evaluate the operations indicated in the numerator and in the denominator: $...=\dfrac{42-28i+15i-10i^{2}}{9-4i^{2}}=...$ Substitute $i^{2}$ by $-1$ and simplify: $...=\dfrac{42-28i+15i-10(-1)}{9-4(-1)}=\dfrac{42-13i+10}{9+4}=...$ $...=\dfrac{52-13i}{13}=\dfrac{52}{13}-\dfrac{13}{13}i=4-i$
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